Let's prepare for RMO #2

Find all positive integers \(n\) for which there exist positive integers \(x,y\) and \(k\) such that \(gcd(x,y)=1,k>1\) and \(3^{n}=x^{k}+y^{k}\).

Submit your answer as sum of all the values of \((x,y,n,k)\).

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